Related papers: Tip-splitting evolution in the idealized Saffman-T…
Using our exact time-depending solutions, we solve the Saffman-Taylor finger selection problem in the absence of surface tension by showing that an arbitrary interface in a Hele-Shaw cell evolves to a single uniformly advancing finger…
The three-layer Saffman-Taylor problem introduces two coupled moving interfaces separating the three fluids. A very recent weakly nonlinear analysis of this problem in a radial Hele-Shaw cell setup has shown that the morphologies of the…
We study the exact non-singular zero-surface tension solutions of the Saffman-Taylor problem for all times. We show that all moving logarithmic singularities a_k(t) in the complex plane \omega = e^{i\phi}, where \phi is the stream function,…
We develop a stream function approach for the horizontal Hele-Shaw, Saffman-Taylor finger. The model yields a nonlinear time-dependent differential equation. The finger widths derived from the equation are $1>\lambda>\frac{1}{\sqrt{5}}$, in…
The selection of Saffman-Taylor fingers by surface tension has been extensively investigated. In this paper we are concerned with the existence and selection of steadily translating symmetric finger solutions in a Hele-Shaw cell by small…
Nonlinear time-dependent differential equations for the Hele-Shaw, Saffman-Taylor problem are derived. The equations are obtained using a separable ansatz expansion for the stream function of the displaced fluid obeying a Darcian flow.…
The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the…
We solve numerically the nonlinear differential equation for the Hele-Shaw, Saffman-Taylor problem derived in the preceding work. Stationary solutions with no free phenomenological parameters are found to fit the measured patterns. The…
The well-studied selection problems involving Saffman-Taylor fingers or Taylor-Saffman bubbles in a Hele-Shaw channel are prototype examples of pattern selection. Exact solutions to the corresponding zero-surface-tension problems exist for…
We study self-similar viscous fingering for the case of divergent flow within a wedge-shaped Hele-Shaw cell. Previous authors have conjectured the existence of a countably-infinite number of selected solutions, each distinguished by a…
We present an analytical study for predicting the finger width of the Saffman-Taylor finger in a tapered Hele-Shaw cell. We consider a rectilinear geometry with a constant depth gradient and apply analytical techniques of singular…
We study the minimal class of exact solutions of the Saffman-Taylor problem with zero surface tension, which contains the physical fixed points of the regularized (non-zero surface tension) problem. New fixed points are found and the basin…
We consider a zero-surface-tension two-dimensional Hele-Shaw flow in an infinite wedge. There exists a self-similar interface evolution in this wedge, an analogue of the famous Saffman-Taylor finger in a channel, exact shape of which has…
A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous…
The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the…
We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $\lambda_1$ and…
We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155…
Fracture processes are ubiquitous in soft materials, even in complex fluids, subjected to stresses. To investigate these processes in a simple geometry, we use a model self-assembled transient gel and study the instability patterns obtained…
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities -…
We address pattern selection problems in nonlinear interface dynamics by maximizing the entropy of the most probable (classical) scenario associated with the processes. This variational principle we applied to well-known selection problems…